If stimulus responses are linearly related to squared distances between stimulus scale values and person scores along a latent continuum, (a) the stimulus × stimulus correlation matrix will display a simplex-like pattern, (b) the signs of first-order partial correlations can be specified in an empirically testable manner, and (c) the variables will have a semicircular, two-factor structure. Along the semicircle, variables will be ordered by their positions on the latent dimension. The above results suggest procedures for examining the appropriateness of the model and procedures for ordering the stimuli. Applications to developmental and attitudinal data are discussed.

Assuming that subject responses rank order stimuli by preference, statistical methods are presented for testing the hypothesis that responses conform to a unidimensional, qualitative unfolding model and to an a priori stimulus ordering. The model postulates that persons and stimulus variables are ordered along a single continuum and that subjects most prefer stimuli nearest their own position. The underlying continuum need not form an interval scale of the stimulus attribute. The general assumptions of the test for the unfolding model make it suitable for the analysis of structure in attitude responses, preference data, and developmental stage data.